AlGaN/GaN based FETs have great potential as sensitive and fast operating detectors because of their material advantages such as high breakdown voltage, high electron mobility, and high saturation velocity. These advantages could be exploited for resonant and non-resonant terahertz detection. We have designed, fabricated, and characterized AlGaN/GaN based FETs as single pixel terahertz detectors. This work focuses on non-resonant detection and imaging using GaN field plate FETs. To evaluate their performances as terahertz detectors, we have measured the responsivity as a function of gate voltage, the azimuthal angle between the terahertz electric field, the source-to-drain direction, and the temperature. A simple analytical model of the response is developed. It is based on plasma density perturbation in the transistor channel by the incoming terahertz radiation. The model shows how the non-resonant detection signal is related to static (dc) transistor characteristics and it fully describes the experimental results on the non-resonant sub-terahertz detection by the AlGaN/GaN based FETs. The imaging performances are evaluated by scanning objects in transmission mode and an example of application of terahertz imaging as new non-destructive technique for the quality control of materials is given. Results indicate that these FETs can be considered as promising devices for terahertz detection and imaging applications.